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A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations. (English) Zbl 1364.76111
Summary: Based on the high order essentially non-oscillatory (ENO) Lagrangian type scheme on quadrilateral meshes presented in our earlier work J. Cheng and Ch.-W. Shu [J. Comput. Phys. 227, No. 2, 1567–1596 (2007; Zbl 1126.76035)], in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics. The main purpose of this work is to demonstrate our claim in [loc. cit.] that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges, which restricts the accuracy of the resulting scheme to at most second order. The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes. Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
35Q31 Euler equations
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